Thanks--my hospital volunteering is more along these lines, reading to patients, sitting with them and talking to them, doing activities with them. I also mentor high school and college students one-on-one through an organization I was involved in creating. I've looked into getting involved in helping unhoused people at a homeless shelter I've volunteered at or with patients at the free clinic but understandably many of those "hands-on" roles require certain training in social work or medicine which I don't have (yet).
I assume (could be wrong, with assuming and all) that he meant something more of being in contact with that at need population.
I'm not sure about the rest of the places, but the homeless shelter near me has opportunities like this that don't require much training. For example, i'm able to check out a basketball and play basketball with them on saturdays. I can work in the computer lab and help people with their resumes/how to use Excel, etc. There are many ways to "help" hands on and get valuable time with the population, which I think is more beneficial. Especially for a younger person, you need to prove that you can interact with populations different from you, empathize and relate to them.
Habitat for Humanity most of the time just wants you to show up to the projects and someone will direct you how to help. Many of my students when I was in the military did this for community service hours and none of them had any homebuilding training of any sort.
In short- there are a lot of ways to get hands on with underserved populations, just be a bit creative. You can teach yoga, meditation, almost anything that you know that could be beneficial. Many places, like homeless shelters, that may not have a program set up like this will be more than willing to let you do something if you propose it to them. From your post and background you sound like a very motivated, intelligent person. I suspect if you propose some way to integrate with the population at a homeless shelter, they would be willing to let you try.
From there, it's just articulating on your application what you did and how it helped/what you learned from it. I suspect adcoms enjoy reading about these outside of the box stories more than the "i handed out blankets and walked patients to their rooms" stories that a lot of us have. (Not that there's anything wrong with this experience, I just assume reading the same thing 4000 times is boring.) Sometimes,
interesting is better. It's important to remember that while we aren't really competing with others for admission, we are competing with others to be memorable to the people on the adcom. 3.8+/515+ isn't rare according to MSAR and isn't catching attention. It's the details that matter and this is how we write those details.